3x^2-18x-98=0

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Solution for 3x^2-18x-98=0 equation: 


Simplifying
3x2 + -18x + -98 = 0

Reorder the terms:
-98 + -18x + 3x2 = 0

Solving
-98 + -18x + 3x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
3 the coefficient of the squared term: 

Divide each side by '3'.
-32.66666667 + -6x + x2 = 0

Move the constant term to the right:

Add '32.66666667' to each side of the equation.
-32.66666667 + -6x + 32.66666667 + x2 = 0 + 32.66666667

Reorder the terms:
-32.66666667 + 32.66666667 + -6x + x2 = 0 + 32.66666667

Combine like terms: -32.66666667 + 32.66666667 = 0.00000000
0.00000000 + -6x + x2 = 0 + 32.66666667
-6x + x2 = 0 + 32.66666667

Combine like terms: 0 + 32.66666667 = 32.66666667
-6x + x2 = 32.66666667

The x term is -6x.  Take half its coefficient (-3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
-6x + 9 + x2 = 32.66666667 + 9

Reorder the terms:
9 + -6x + x2 = 32.66666667 + 9

Combine like terms: 32.66666667 + 9 = 41.66666667
9 + -6x + x2 = 41.66666667

Factor a perfect square on the left side:
(x + -3)(x + -3) = 41.66666667

Calculate the square root of the right side: 6.454972244

Break this problem into two subproblems by setting 
(x + -3) equal to 6.454972244 and -6.454972244.


Subproblem 1
x + -3 = 6.454972244

Simplifying
x + -3 = 6.454972244

Reorder the terms:
-3 + x = 6.454972244

Solving
-3 + x = 6.454972244

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '3' to each side of the equation.
-3 + 3 + x = 6.454972244 + 3

Combine like terms: -3 + 3 = 0
0 + x = 6.454972244 + 3
x = 6.454972244 + 3

Combine like terms: 6.454972244 + 3 = 9.454972244
x = 9.454972244

Simplifying
x = 9.454972244


Subproblem 2
x + -3 = -6.454972244

Simplifying
x + -3 = -6.454972244

Reorder the terms:
-3 + x = -6.454972244

Solving
-3 + x = -6.454972244

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '3' to each side of the equation.
-3 + 3 + x = -6.454972244 + 3

Combine like terms: -3 + 3 = 0
0 + x = -6.454972244 + 3
x = -6.454972244 + 3

Combine like terms: -6.454972244 + 3 = -3.454972244
x = -3.454972244

Simplifying
x = -3.454972244


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {9.454972244, -3.454972244}

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